| As the storage and computational capabilities of classical computers gradually approach their limits,quantum computing with“quantum supremacy”has emerged as a promising approach to address this challenge.Quantum Phase Estimation(QPE)is an indispensable component of numerous quantum algorithms,and the efficient and accurate QPE algorithms play a crucial role in enhancing the performance of quantum algorithms.In this thesis,we explore the application of Simulated Annealing(SA)algorithm and Recurrent Neural Networks(RNN)from the field of machine learning to QPE.The main results are the following:(1)A Simulated Annealing-based Quantum Phase Estimation(SA-QPE)algorithm is proposed in this thesis that integrates the Simulated Annealing(SA)technique into the updating strategy of Adaptive Quantum Phase Estimation(AQPE)circuits.By employing SA,a set of solution vectors with a length of N can be obtained,which are incorporated into the updating strategy for phase estimation.The performance of the solution vectors is evaluated using the Holevo variance.To prevent the algorithm from getting trapped in local optima,Mentropolis criterion is introduced to selectively preserves solutions with larger variances with a certain probability.Through numerical simulations,we validate the effectiveness of the SA-QPE algorithm and compare its performance with Differential Evolution-based QPE(DE-QPE)and Particle Swarm Optimization-based QPE(PSO-QPE).The results show that,for the same solution vector length,SA-QPE achieves an average performance improvement of 0.129 and 0.181(measured by the Holevo variance)over DE-QPE and PSO-QPE,respectively in the absence of noise.When Gaussian noise is introduced,the performance improvement becomes greater as the variance of the Gaussian noise increases.When?=0.2,SA-QPE outperforms DE-QPE and PSO-QPE with average performance improvements of 0.184 and0.174,respectively.When?=0.4,SA-QPE achieves average performance improvements of 0.195and 0.242 over DE-QPE and PSO-QPE,respectively.Moreover,even in the presence of telegraph noise,SA-QPE demonstrates a superior performance compared to with those of DE-QPE and PSO-QPE.(2)A Recurrent Neural Networks-based Quantum Phase Estimation(RNN-QPE)algorithm is then presented by taking advantage of the superior time-series processing capabilities of RNN.Considering the evident time-series characteristics in the multiple runs of AQPE for the same phase value,we integrate RNN into AQPE.The RNN takes the input quantum bit states and measurement results of the AQPE circuit at each iteration and generates the sine and cosine function values of the phase as outputs.The Mean Square Error(MSE)between the network’s output and the true sine and cosine function values of the phase is computed,and the parameters are optimized by using the Adam W optimizer.The simulation results show that the proposed RNN-QPE outperforms SA-QPE in phase estimation.As measured by the Holevo variance ln(_HV),RNN-QPE achieves an average performance improvement of 0.174 compared to SA-QPE in the absence of noise.Additionally,RNN-QPE exhibits enhanced robustness,with average performance improvements of 0.494 under Gaussian noise and 0.390 under telegraph noise compared to SA-QPE.Moreover,RNN-QPE significantly reduces the time complexity compared to SA-QPE from(N ~3)to(N),leading to a substantial reduction in algorithm execution time. |
